Elliptic curve data - 20475.r3

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '20475q', 'Clabel': '20475q2', 'Cnumber': 2, 'abc_quality': 0.9579816735246167, 'absD': 8583644671875, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 8190, 'ainvs': [0, 0, 1, 2850, -128219], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 20475, 'degree': 31104, 'elladic_images': ['3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1648227978334928411004603820', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3], 'jinv': [224755712, 753571], 'lmfdb_iso': '20475.r', 'lmfdb_label': '20475.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 13, 42], 'min_quad_twist_disc': -15, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '15.24.0-3.a.1.1', '117.36.0.?', '182.2.0.?', '546.24.1.?', '585.72.0.?', '1638.72.3.?', '2730.48.1.?', '8190.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 25], [5, 14, 819], [7, 8, 2925], [13, 14, 1575]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18920230271761219189754190307', 'prec': 107}, 'szpiro_ratio': 3.73187078576903, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 4, -6, 0, -7, 0], 'aplist': [0, 0, 0, -1, 0, -1, -6, -7, 3, 9, 5, -2, 6, 1, 3, -9, 0, -10, -14, 6, -11, -1, 3, -15, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 20475, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '20475.r', 'trace_hash': 2026066408559903478}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.097330235234898259509522473057', 'prec': 107}, 'conductor': 20475, 'gens': [], 'heights': [], 'lmfdb_label': '20475.r3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37449349290749302827832571125', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.74898698581498605655665142250378678622', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [18, 3, 0], '3': 'a', '5': 'a', '7': [0, 0], '11': [0, 0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [2, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '20475.r3'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 1045701
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '20475.r3', 'torsion': [3]}
  • id: 1045702
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '20475.r3', 'torsion': [3]}
  • id: 1045703
    {'degree': 3, 'field': [-2, 4, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [2]}
  • id: 1045704
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '20475.r3', 'torsion': [3, 3]}
  • id: 1045706
    {'degree': 6, 'field': [-4, -8, 16, -8, 12, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [6]}
  • id: 1045705
    {'degree': 6, 'field': [9, -33, 44, -23, 14, -3, 1], 'lmfdb_label': '20475.r3', 'torsion': [2, 2]}
  • id: 1045707
    {'degree': 6, 'field': [34, -94, 82, -37, 23, -3, 1], 'lmfdb_label': '20475.r3', 'torsion': [6]}
  • id: 1045708
    {'degree': 12, 'field': [-4218674, 633976, 7432176, 2568932, -725132, -40992, 120580, -4992, -2064, -134, 4, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [4]}
  • id: 1045709
    {'degree': 12, 'field': [16, -32, 128, 192, 240, -64, -136, 104, 128, -16, -12, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [3, 6]}
  • id: 1045711
    {'degree': 12, 'field': [121, 0, 559, 0, 4646, 0, 2947, 0, 602, 0, 43, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [2, 6]}
  • id: 1045710
    {'degree': 12, 'field': [2916, 0, -2996, 0, 376, 0, 347, 0, 107, 0, 13, 0, 1], 'lmfdb_label': '20475.r3', 'torsion': [2, 6]}
  • id: 1045712
    {'degree': 18, 'field': [-1086749, 24499929, -33156600, 31618715, -4863804, 4487940, -1521261, 973413, 468411, -353355, 99270, -31827, 8886, -5145, 771, 574, -69, -9, 1], 'lmfdb_label': '20475.r3', 'torsion': [9]}
  • id: 1045713
    {'degree': 18, 'field': [423025, -826575, 1586055, -2214260, 2431869, -2195274, 1649398, -1054359, 595908, -294358, 133410, -52827, 19285, -5949, 1665, -366, 72, -9, 1], 'lmfdb_label': '20475.r3', 'torsion': [9]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 465221
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '20475.r3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 465222
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '20475.r3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 465223
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '20475.r3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 465224
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '20475.r3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1800998
    {'adelic_gens': [[1, 18, 0, 1], [4913, 0, 0, 8189], [1, 9, 9, 82], [8179, 1620, 1800, 629], [8173, 18, 8172, 19], [4426, 3285, 2025, 76], [1, 6, 6, 37], [1, 0, 18, 1], [1, 12, 0, 1], [2116, 3285, 225, 4906]], 'adelic_image': '8190.144.3.?', 'conductor': 20475, 'lmfdb_label': '20475.r3', 'prime': 0}
  • id: 95421
    {'conductor': 20475, 'elladic_image': '3.12.0.1', 'lmfdb_label': '20475.r3', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 20475.r does not appear in ec_padic